Hall Effect, Magnetoresistance, and Size Effects in Copper

Measurements of the Hall coefficient of several annealed polycrystalline Cu strips of resistivity ratio $\frac{\rho \left(273\mathrm{}°\mathrm{K}\right)}{\rho \left(4.2\mathrm{}°\mathrm{K}\right)}\sim 450$ and thicknesses ranging from 0.05 to 1.6 mm have revealed the existence of a marked size effect at low temperatures. The effect is orders of magnitude greater than that to be expected on the basis of free-electron theory. It is suggested that earlier low-temperature data on the Hall effect of thin high-purity samples are subject to uncertainties arising from such effects. Size effects were also evident in the transverse magnetoresistance. At high fields, a tendency toward saturation in the transverse magnetoresistance was observed for thick samples. The temperature dependence of the Hall coefficient has also been studied.